Quantum coherence is a critical resource for many operational tasks. Understanding how to quantify and manipulate it also promises to have applications for a diverse set of problems in theoretical physics. For certain applications, however, one requires coherence between the eigenspaces of specific physical observables, such as energy, angular momentum, or photon number, and it makes a difference which eigenspaces appear in the superposition. For others, there is a preferred set of subspaces relative to which coherence is deemed a resource, but it is irrelevant which of the subspaces appear in the superposition. We term these two types of coherence unspeakable and speakable, respectively. We argue that a useful approach to quantifying and characterizing unspeakable coherence is provided by the resource theory of asymmetry when the symmetry group is a group of translations, and we translate a number of prior results on asymmetry into the language of coherence. We also highlight some of the applications of this approach, for instance, in the context of quantum metrology, quantum speed limits, quantum thermodynamics, and nuclear magnetic resonance (NMR). The question of how best to treat speakable coherence as a resource is also considered. We review a popular approach in terms of operations that preserve the set of incoherent states, propose an alternative approach in terms of operations that are covariant under dephasing, and we outline the challenge of providing a physical justification for either approach. Finally, we note some mathematical connections that hold among the different approaches to quantifying coherence.

The prospect of quantum-simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudospins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in $(1+1)$ space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of microtraps. The second scheme represents the gauge fields by spins $\frac{1}{2}$, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting small-scale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.

We simulate the decay dynamics of an isolated monopole defect in the nematic vector of a spin-1 Bose-Einstein condensate during the polar-to-ferromagnetic phase transition of the system. Importantly, the decay of the monopole occurs in the absence of external magnetic fields and is driven principally by the dynamical instability due to the ferromagnetic spin-exchange interactions. An initial isolated monopole is observed to relax into a polar-core spin vortex, thus demonstrating the spontaneous transformation of a point defect of the polar order parameter manifold to a line defect of the ferromagnetic manifold. We also investigate the dynamics of an isolated monopole pierced by a quantum vortex line with winding number $\kappa$. It is shown to decay into a coreless Anderson-Toulouse vortex if $\kappa =1$ and into a singular vortex with an empty core if $\kappa =2$. In both cases, the resulting vortex is also encircled by a polar-core vortex ring.

We investigate the dispersion relations for light coupled to one-dimensional ensembles of atoms with different level schemes. The unifying feature of all the considered setups is that the forward and backward propagating quantum fields are coupled by the applied classical drives such that the group velocity can vanish in an effect known as “stationary light.” We derive the dispersion relations for all the considered schemes, highlighting the important differences between them. Furthermore, we show that additional control of stationary light can be obtained by treating atoms as discrete scatterers and placing them at well-defined positions. For the latter purpose, a multimode transfer matrix theory for light is developed.

We study the monopole (breathing) mode of a finite temperature Bose-Einstein condensate in an isotropic harmonic trap recently developed by Lobser et al. [Nat. Phys. 11, 1009 (2015)]. We observe a nonexponential collapse of the amplitude of the condensate oscillation followed by a partial revival. This behavior is identified as being due to beating between two eigenmodes of the system, corresponding to in-phase and out-of-phase oscillations of the condensed and noncondensed fractions of the gas. We perform finite temperature simulations of the system dynamics using the Zaremba-Nikuni-Griffin methodology [J. Low Temp. Phys. 116, 277 (1999)], and find good agreement with the data, thus confirming the two mode description.

We report on an observation of stationary light pulses and narrowband light storage inside a hollow-core photonic crystal fiber. Laser-cooled atoms were first loaded into the fiber core, providing strong light-matter coupling. Light pulses were then stored in a collective atomic excitation using a single control laser beam. By applying a second counterpropagating control beam, a light pulse could be brought to a standstill. Our work paves the way towards the creation of strongly correlated many-body systems with photons and applications in the field of quantum information processing.

Despite the tremendous progress in wave front shaping for enhancing imaging penetration depths in scattering media, several factors, among which are significantly low signal-to-noise ratios at large depths, prevent feasibility for nonlinear imaging in biological tissues. Here, we propose an alternative to the traditional schemes that use optimization of a nonlinear signal. By exploiting the linear photons instead of nonlinearly generated ones, we show strong enhancements of nonlinear signals of several orders of magnitude, through thicknesses of a few transport mean free paths, which corresponds to millimeters in biological tissues. This is achieved by measuring the linear broadband transmission matrix (TM) of the scattering medium, using a spectral bandwidth comparable to the speckle spectral correlation width. We further highlight several advantages of the use of linear TM for prospective nonlinear imaging deep inside scattering media.

Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and it is applicable to all experimental systems with long-range interactions: trapped ions, polar molecules, Rydberg atoms, nitrogen-vacancy centers, and cavity QED. Our approach allows one achieve a short-range interaction without relying on Hubbard superexchange.

Recent experiments have revealed the formation of stable droplets in dipolar Bose-Einstein condensates. This surprising result has been explained by the stabilization given by quantum fluctuations. We study in detail the properties of a Bose-Einstein condensate in the presence of quantum stabilization. The ground-state phase diagram presents three main regimes: mean-field regime, in which the quantum correction is perturbative; droplet regime, in which quantum stabilization is crucial; and a multistable regime. In the absence of a multistable region, the condensate undergoes a crossover from the mean-field to the droplet solution marked by a characteristic growth of the peak density that may be employed to clearly distinguish quantum stabilization from other stabilization mechanisms. Interestingly, quantum stabilization allows for three-dimensionally self-bound condensates. We characterized these self-bound solutions, and discuss their realization in experiments. We conclude with a discussion of the lowest-lying excitations both for trapped condensates, and for self-bound solutions.

The photon-ion merged-beam technique was used at a synchrotron light source for measuring the absolute cross sections of the double and triple photodetachment of ${\mathrm{O}}^{-}$ ions. The experimental photon energy range of 524–543 eV comprised the threshold for $K$-shell ionization. Using resolving powers of up to 13 000, the position, strength, and width of the below-threshold $1s2s^{2}2p^6 {}^{2}S$ resonance as well as the positions of the $1s2s^{2}2p^5 {}^{3}P$ and $1s2s^{2}2p^5 {}^{1}P$ thresholds for $K$-shell ionization were determined with high precision. In addition, systematically enlarged multiconfiguration Dirac-Fock calculations have been performed for the resonant detachment cross sections. Results from these ab initio computations agree very well with the measurements for the widths and branching fractions for double and triple detachment, if double shakeup (and shakedown) of the valence electrons and the rearrangement of the electron density is taken into account. For the absolute cross sections, however, a previously found discrepancy between measurements and theory is confirmed.

One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as generalized Gibbs ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general one-dimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348, 207 (2015)] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex $P$-representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.

We report on electron momentum distributions from single ionization of Ar in strong orthogonally polarized two-color (OTC) laser fields measured with the COLTRIMS technique. We study the effect of Coulomb focusing whose signature is a cusplike feature in the center of the electron momentum spectrum. While the direct electrons show the expected strong dependence on the phase between the two colors, surprisingly the Coulomb-focused structure is almost not influenced by the weak second harmonic streaking field. This effect is explained by the use of a CTMC simulation which describes the tunneled electron wave packet in terms of classical trajectories under the influence of the combined Coulomb and OTC laser field. We find a subtle interplay between the initial momentum of the electron upon tunneling, the ionization phase and the action of the Coulomb field that makes the Coulomb focused part of the momentum spectrum apparently insensitive to the weaker streaking field.

The influence of the center-of-mass motion of a trapped two-level system on efficient resonant single-photon absorption is investigated. It is shown that this absorption process depends strongly on the ratio between the characteristic time scales of spontaneous photon emission and of the two-level system's center-of-mass motion. In particular, if the spontaneous photon emission process occurs almost instantaneously on the time scale of the center-of-mass motion, coherent control of the center-of-mass motion offers interesting perspectives for optimizing single-photon absorption. It is demonstrated that time-dependent modulation of a harmonic trapping frequency allows to squeeze the two-level system's center-of-mass motion so strongly that high efficient single-photon absorption is possible even in cases of weak confinement by a trapping potential.

We report on the Earth's rotation measurement using a K-Rb-${}^{21}\mathrm{Ne}$ comagnetometer. The steady-state responses of the nuclear- and electronic-spin polarizations therein have been shown. The light shift arising from the circularly polarized pump laser beam enables the comagnetometer to sense dual-axis rotations. This feasibility has been emphasized and verified by numerical simulation. We believe that this sensor could be used in any application requiring compact size, low cost, and high-precision inertial navigation.

We investigate the conditions for the emergence of wave instabilities in a vacuum cavity delimited by cylindrical metallic walls under rotation. It is shown that for a small vacuum gap and for an angular velocity exceeding a certain threshold, the interactions between the surface plasmon polaritons supported by each wall give rise to unstable behavior of the electromagnetic field manifested in exponential growth with time. The instabilities occur only for certain modes of oscillation and are due to the transformation of kinetic energy into electromagnetic energy. We also study the possibility of having asymmetric light flows and optical isolation relying on the relative motion of the cavity walls.

We show that the vibrations of an ion Coulomb crystal can be cooled to the zero-point motion through the optomechanical coupling with a high-finesse cavity. Cooling results from the interplay between coherent scattering of cavity photons by the ions, which dynamically modifies the vibrational spectrum, and cavity losses, that dissipate motional energy. The cooling mechanism we propose requires that the length scales of the crystal and the cavity are mismatched so that the system is intrinsically frustrated, leading to the formation of defects (kinks). When the pump is strong enough, the anti-Stokes sidebands of all vibrational modes can be simultaneously driven. These dynamics can be used to prepare ground-state chains of dozens of ions within tens of milliseconds in state-of-the-art experimental setups. In addition, we identify parameter regimes of the optomechanical interactions where individual localized modes can be selectively manipulated, and monitored through the light at the cavity output. These dynamics exemplify robust quantum reservoir engineering of strongly correlated mesoscopic systems and could find applications in optical cooling of solids.

We reexamine the invariance of two-photon transition matrix elements and corresponding two-photon Rabi frequencies under the “gauge” transformation from the length to the velocity gauge. It is shown that gauge invariance, in the most general sense, only holds at exact resonance, for both one-color as well as two-color absorption. The arguments leading to this conclusion are supported by analytic calculations which express the matrix elements in terms of hypergeometric functions, and ramified by a “master identity” which is fulfilled by off-diagonal matrix elements of the Schrödinger propagator under the transformation from the velocity to the length gauge. The study of the gauge dependence of atomic processes highlights subtle connections between the concept of asymptotic states, the gauge transformation of the wave function, and infinitesimal damping parameters for perturbations and interaction Hamiltonians that switch off the terms in the infinite past and future [of the form $exp(-\epsilon |t\left|\right)]$. We include a pertinent discussion.

Classical correlation can be locked via quantum means: quantum data locking. With a short secret key, one can lock an exponentially large amount of information in order to make it inaccessible to unauthorized users without the key. Quantum data locking presents a resource-efficient alternative to one-time pad encryption which requires a key no shorter than the message. We report experimental demonstrations of a quantum data locking scheme originally proposed by D. P. DiVincenzo et al. [Phys. Rev. Lett. 92, 067902 (2004)] and a loss-tolerant scheme developed by O. Fawzi et al. [J. ACM 60, 44 (2013)]. We observe that the unlocked amount of information is larger than the key size in both experiments, exhibiting strong violation of the incremental proportionality property of classical information theory. As an application example, we show the successful transmission of a photo over a lossy channel with quantum data (un)locking and error correction.

Shannon proved in 1949 that information-theoretic-secure encryption is possible if the encryption key is used only once, is random, and is at least as long as the message itself. Notwithstanding, when information is encoded in a quantum system, the phenomenon of quantum data locking allows one to encrypt a message with a shorter key and still provide information-theoretic security. We present one of the first feasible experimental demonstrations of quantum data locking for direct communication and propose a scheme for a quantum enigma machine that encrypts 6 bits per photon (containing messages, new encryption keys, and forward error correction bits) with less than 6 bits per photon of encryption key while remaining information-theoretically secure.